Grey system model with the fractional order accumulation

► We extend the traditional accumulation (with integer order) to fractional order accumulation in Grey system modelling. ► The relationship between the accumulation order number and the memory property of the GM (1,1) is discussed. ► The results of practical numerical examples demonstrate that this method provides very remarkable predication performance. The perturbation theory of least squares method is applied to explain why the traditional accumulated generating operator violates the principle of new information priority of Grey system theory. A new Grey system model with the fractional order accumulation is put forward and the priority of new information can be better reflected when the accumulation order number becomes smaller in the in-sample model. But Grey system model cannot deal with the systems with memory when the accumulation order number is 0 in the in-sample model. The results of practical numerical examples demonstrate that the new Grey model provides very remarkable predication performance compared with the traditional Grey model for small sample.